"Two magnitudes whether commensurable or incommensurable, balance at distances reciprocally proportional to the magnitudes." (Archimedes, On the Equilibrium of Planes Vol. I, 3rd century BC)
"Inequality is the cause of all local movements. There is no rest without equality." (Leonardo da Vinci, "Codex Atlanticus", 1478)
"There must be a double method for solving mechanical problems: one is the direct method founded on the laws of equilibrium or of motion; but the other one is by knowing which formula must provide a maximum or a minimum. The former way proceeds by efficient causes: both ways lead to the same solution, and it is such a harmony which convinces us of the truth of the solution, even if each method has to be separately founded on indubitable principles. But is often very difficult to discover the formula which must be a maximum or minimum, and by which the quantity of action is represented.” (Leonhard Euler, “Specimen de usu observationum in mathesi pura”, Novi Commentarii academiae scientiarum Petropolitanae 6, 1756/57)
"Statics is the science of the equilibrium of forces. In general, force or power is the cause, whatever it may be, which induces or tends to impart motion to the body to which it is applied. The force or power must be measured by the quantity of motion produced or to be produced. In the state of equilibrium, the force has no apparent action. It produces only a tendency for motion in the body it is applied to. But it must be measured by the effect it would produce if it were not impeded. By taking any force or its effect as unity, the relation of every other force is only a ratio, a mathematical quantity, which can be represented by some numbers or lines. It is in this fashion that forces must be treated in mechanics." (Joseph-Louis de Lagrange, "Mechanique Analytique", 1788)
"Demand and supply are the opposite extremes of the beam, whence depend the scales of dearness and cheapness; the price is the point of equilibrium, where the momentum of the one ceases, and that of the other begins." (Jean-Baptiste Say, T"raité d'économie politique" ["A Treatise On Political Economy"] Vol. II, 1803)
"The production of motion in the steam engine always occurs in circumstances which it is necessary to recognize, namely when the equilibrium of caloric is restored, or (to express this differently) when caloric passes from the body at one temperature to another body at a lower temperature." (Nicolas Léonard S Carnot, "Réflexions sur la Puissance Motrice du Feu et sur les Machines Propres a Développer cette Puissance", 1824)
"The state of crisis is the real war; the equilibrium is nothing but its reflex." (Carl von Clausewitz, "On War", 1832)
"The determination of the average man is not merely a matter of speculative curiosity; it may be of the most important service to the science of man and the social system. It ought necessarily to precede every other inquiry into social physics, since it is, as it were, the basis. The average man, indeed, is in a nation what the centre of gravity is in a body; it is by having that central point in view that we arrive at the apprehension of all the phenomena of equilibrium and motion." (Adolphe Quetelet, "A Treatise on Man and the Development of his Faculties", 1842)
"Everything lives by movement, everything is maintained by equilibrium, and harmony results from the analogy of contraries; this law is the form of forms. (Eliphas Levi, Transcendental Magic, 1854)
"Living things have no inertia, and tend to no equilibrium." (Thomas H Huxley, "On the Educational Value of the Natural History Sciences", 1854)
"[...] the small is great, the great is small; all is in equilibrium in necessity […]" (Victor Hugo, Les Misérables, 1862
"Nature! […] She creates needs because she loves action. Wondrous! that she produces all this action so easily. Every need is a benefit, swiftly satisfied, swiftly renewed. - Every fresh want is a new source of pleasure, but she soon reaches an equilibrium." Johann Wolfgang von Goethe, Nature, 1870)
"We cannot prevent equilibrium from producing its effects. We may brave human laws, but we cannot resist natural ones." (Jules Verne, "Twenty Thousand Leagues Under the Sea", 1870)
"Any system in stable chemical equilibrium, subjected to the influence of an external cause tends to change either its temperature or its condensation (pressure, concentration, number of molecules in unit volume), either as a whole or in some of its parts, can only undergo such internal modifications as would, if produced alone, bring about a change of temperature or of condensation of opposite sign to that resulting from the external cause." (Henri L Le Chatelier, "A General Statement of the Laws of Chemical Equilibrium", Comptes rendus Vol. 99, 1884)
"Every situation is an equilibrium of forces; every life is a struggle between opposing forces working within the limits of a certain equilibrium." (Henri-Frédéric Amiel, "Amiel's Journal", 1885)
"Plasticity, then, in the wide sense of the word, means the possession of a structure weak enough to yield to an influence, but strong enough not to yield all at once. Each relatively stable phase of equilibrium in such a structure is marked by what we may call a new set of habits." (William James, "The Laws of Habit", 1887)
"Every change of one of the factors of an equilibrium occasions a rearrangement of the system in such a direction that the factor in question experiences a change in a sense opposite to the original change." (Henri L Le Chatelier, "Recherches Experimentales et Theoriques sur les Equilibres Chimiques" ["Experimental and Theoretical Research on Chemical Equilibria"], Annales des Mines 8, 1888)
"In every symmetrical system every deformation that tends to destroy the symmetry is complemented by an equal and opposite deformation that tends to restore it. […] One condition, therefore, though not an absolutely sufficient one, that a maximum or minimum of work corresponds to the form of equilibrium, is thus applied by symmetry." (Ernst Mach, "The Science of Mechanics: A Critical and Historical Account of Its Development", 1893)
"That branch of physics which is at once the oldest and the simplest and which is therefore treated as introductory to other departments of this science, is concerned with the motions and equilibrium of masses. It bears the name of mechanics." (Ernst Mach, "The Science of Mechanics: A Critical and Historical Account of Its Development", 1893)
"The whole aspect of the universe changes with this new conception. The idea of force governing the world, of pre-established law, preconceived harmony, disappears to make room for the harmony that [Charles] Fourier had caught a glimpse of: the one which results from the disorderly and incoherent movements of numberless hosts of matter, each of which goes its own way and all of which hold each other in equilibrium." (Peter Kropotkin, "Anarchism: Its Philosophy and Ideal", 1896)
"When we study the structure of the atom, we shall arrive at the conclusion that it is an immense reservoir of energy solely constituted by a system of imponderable elements maintained in equilibrium by the rotations, attractions and repulsions of its component parts." (Gustave Le Bon, "The Evolution of Matter", 1907)
"All thinking is of disturbance, dynamical, a state of unrest tending towards equilibrium. It is all a mode of classifying and of criticising with a view of knowing whether it gives us, or is likely to give us, pleasure or no." (Samuel Butler, "Thinking - The Note-Books of Samuel Butler", 1912)
"The network of ideas remains and forms as it were a moving cobweb in which repose wriggles and tosses, incapable of finding a stable equilibrium." (Jean H Fabre, "The Life of the Fly", 1913)
"We rise from the conception of form to an understanding of the forces which gave rise to it [...] in the representation of form we see a diagram of forces in equilibrium, and in the comparison of kindred forms we discern the magnitude and the direction of the forces which have sufficed to convert the one form into the other." (D'Arcy Wentworth Thompson, "On Growth and Form" Vol. 2, 1917)
"A society in stable equilibrium is - by definition - one that has no history and wants no historians." (Henry Adams, "The Degradation of the Democratic Dogma", 1919)
"All biologic phenomena act to adjust: there are no biologic actions other than adjustments. Adjustment is another name for Equilibrium. Equilibrium is the Universal, or that which has nothing external to derange it." (Charles Fort, The Book of the Damned, 1919)
"Since the atom, as a whole, is neutral, there must be a positive charge associated with the atom equal in amount to the sum of the negative charges. The electrical forces between the positive and negative charges preserve the equilibrium of the atom." (James Chadwick, "Radioactivity And Radioactive Substances", 1921)
"The circle is the synthesis of the greatest oppositions. It combines the concentric and the eccentric in a single form and in equilibrium. Of the three primary forms [triangle, square, circle], it points most clearly to the fourth dimension." (Wassily Kandinsky, [letter] 1926)
"Order is not pressure which is imposed on society from without, but an equilibrium which is set up from within." (José Ortega y Gasset, "Mirabeau and Politics", 1927)
"What in the whole denotes a causal equilibrium process, appears for the part as a teleological event." (Ludwig von Bertalanffy, 1929)
"The change from one stable equilibrium to the other may take place as the result of the isolation of a small unrepresentative group of the population, a temporary change in the environment which alters the relative viability of different types, or in several other ways." (John B S Haldane, "The Causes of Evolution", 1932)
"True equilibria can occur only in closed systems and that, in open systems, disequilibria called ‘steady states’, or ‘flow equilibria’ are the predominant and characteristic feature. According to the second law of thermodynamics a closed system must eventually attain a time-independent equilibrium state, with maximum entropy and minimum free energy. An open system may, under certain conditions, attain a time-independent state where the system remains constant as a whole and in its phases, though there is a continuous flow of component materials. This is called a steady state. Steady states are irreversible as a whole. […] A closed system in equilibrium does not need energy for its preservation, nor can energy be obtained from it. In order to perform work, a system must be in disequilibrium, tending toward equilibrium and maintaining a steady state, Therefore the character of an open system is the necessary condition for the continuous working capacity of the organism." (Ludwig on Bertalanffy, "Theoretische Biologie: Band 1: Allgemeine Theorie, Physikochemie, Aufbau und Entwicklung des Organismus", 1932)
"Unaided common sense may indicate an equilibrium, but rarely, if ever, tells us whether it is stable. If much of the investigation here summarised has only proved the obvious, the obvious is worth proving when this can be done. And if the relative importance of selection and mutation is obvious, it has certainly not always been recognised as such." (John B S Haldane, "The Causes of Evolution", 1932)
"The general theory of economic equilibrium was strengthened and made effective as an organon of thought by two powerful subsidiary conceptions - the Margin and Substitution. The notion of the Margin was extended beyond Utility to describe the equilibrium point in given conditions of any economic factor which can be regarded as capable of small variations about a given value, or in its functional relation to a given value." (John Maynard Keynes, "Essays In Biography", 1933)
"A state of equilibrium in a system does not mean, further, that the system is without tension. Systems can, on the contrary, also come to equilibrium in a state of tension (e.g., a spring under tension or a container with gas under pressure). The occurrence of this sort of system, however, presupposes a certain firmness of boundaries and actual segregation of the system from its environment (both of these in a functional, not a spatial, sense). If the different parts of the system are insufficiently cohesive to withstand the forces working toward displacement (i.e., if the system shows insufficient internal firmness, if it is fluid), or if the system is not segregated from its environment by sufficiently firm walls but is open to its neighboring systems, stationary tensions cannot occur. Instead, there occurs a process in the direction of the forces, which encroaches upon the neighboring regions with diffusion of energy and which goes in the direction of an equilibrium at a lower level of tension in the total region. The presupposition for the existence of a stationary state of tension is thus a certain firmness of the system in question, whether this be its own inner firmness or the firmness of its walls." (Kurt Lewin, "A Dynamic Theory of Personality", 1935)
"The process moves in the direction of a state of equilibrium only for the system as a whole. Part processes may at the same time go on in opposed directions, a circumstance which is of the greatest significance for, for example, the theory of detour behavior. It is hence important to take the system whole which is dominant at the moment as basis." (Kurt Lewin, "A Dynamic Theory of Personality", 1935)
"Vertical and horizontal lines are the expression of two opposing forces; they exist everywhere and dominate everything; their reciprocal action constitutes 'life'. I recognized that the equilibrium of any particular aspect of nature rests on the equivalence of its opposites." (Piet M Peintre," Art and Pure Plastic Art", 1937)
"For the state centralisation is the appropriate form of organisation, since it aims at the greatest possible uniformity in social life for the maintenance of political and social equilibrium. But for a movement whose very existence depends on prompt action at any favourable moment and on the independent thought and action of its supporters, centralism could but be a curse by weakening its power of decision and systematically repressing all immediate action. [...] Organisation is, after all, only a means to an end. When it becomes an end in itself, it kills the spirit and the vital initiative of its members and sets up that domination by mediocrity which is the characteristic of all bureaucracies." (Rudolf Rocker, "Anarcho-Syndicalism", 1938)
"One may generalize upon these processes in terms of group equilibrium. The group may be said to be in equilibrium when the interactions of its members fall into the customary pattern through which group activities are and have been organized. The pattern of interactions may undergo certain modifications without upsetting the group equilibrium, but abrupt and drastic changes destroy the equilibrium." (William F Whyte, "Street Corner Society", 1943)
"How would we express in terms of the statistical theory the marvelous faculty of a living organism, by which it delays the decay into thermodynamical equilibrium (death)? [...] the device by which an organism maintains itself stationary at a fairly high level of orderliness […] really consists in continually sucking orderliness from its environment." (Erwin Schrödinger, "What Is Life?", 1944)
"A well ordered society would be one where the State only had a negative action, comparable to that of a rudder: a light pressure at the right moment to counteract the first suggestion of any loss of equilibrium." (Simone Weil, "Gravity and Grace", 1947)
"The behavior of two individuals, consisting of effort which results in output, is considered to be determined by a satisfaction function which depends on remuneration (receiving part of the output) and on the effort expended. The total output of the two individuals is not additive, that is, together they produce in general more than separately. Each individual behaves in a way which he considers will maximize his satisfaction function. Conditions are deduced for a certain relative equilibrium and for the stability of this equilibrium, i.e., conditions under which it will not pay the individual to decrease his efforts. In the absence of such conditions ‘exploitation’ occurs which may or may not lead to total parasitism." (Anatol Rapoport, "Mathematical theory of motivation interactions of two individuals," The Bulletin of Mathematical Biophysics 9, 1947)
"The general method involved may be very simply stated. In cases where the equilibrium values of our variables can be regarded as the solutions of an extremum (maximum or minimum) problem, it is often possible regardless of the number of variables involved to determine unambiguously the qualitative behavior of our solution values in respect to changes of parameters." (Paul Samuelson, "Foundations of Economic Analysis", 1947)
"The study of the conditions for change begins appropriately with an analysis of the conditions for no change, that is, for the state of equilibrium." (Kurt Lewin, "Quasi-Stationary Social Equilibria and the Problem of Permanent Change", 1947)
"Now a system is said to be at equilibrium when it has no further tendency to change its properties." (Walter J Moore, "Physical chemistry", 1950)
"Physical irreversibility manifests itself in the fact that, whenever the system is in a state far removed from equilibrium, it is much more likely to move toward equilibrium, than in the opposite direction." (William Feller, "An Introduction To Probability Theory And Its Applications", 1950)
"Equilibrium requires that the whole of the structure, the form of its elements, and the means of interconnection be so combined that at the supports there will automatically be produced passive forces or reactions that are able to balance the forces acting upon the structures, including the force of its own weight." (Eduardo Torroja, "Philosophy of Structure", 1951)
"[…] there are three different but interconnected conceptions to be considered in every structure, and in every structural element involved: equilibrium, resistance, and stability." (Eduardo Torroja, "Philosophy of Structure" , 1951)
"Business-cycle theorists concerned themselves with why the economy naturally generated fluctuations in employment and output, [while the rest of the profession] continued to operate on the assumption that full employment was the natural, equilibrium position for the economy." (Robert A Gordon, "Business Fluctuations", 1952)
"Biological communities are systems of interacting components and thus display characteristic properties of systems, such as mutual interdependence, self-regulation, adaptation to disturbances, approach to states of equilibrium, etc." (Ludwig von Bertalanffy, "Problems of Life", 1952)
"Every stable system has the property that if displaced from a state of equilibrium and released, the subsequent movement is so matched to the initial displacement that the system is brought back to the state of equilibrium. A variety of disturbances will therefore evoke a variety of matched reactions." (W Ross Ashby, "Design for a Brain: The Origin of Adaptive Behavior", 1952)
"The primary fact is that all isolated state-determined dynamic systems are selective: from whatever state they have initially, they go towards states of equilibrium. These states of equilibrium are always characterised, in their relation to the change-inducing laws of the system, by being exceptionally resistant." (W Ross Ashby, "Design for a Brain: The Origin of Adaptive Behavior", 1952)
"Vertical and horizontal lines are the expression of two opposing forces; they exist everywhere and dominate everything; their reciprocal action constitutes 'life'. I recognized that the equilibrium of any particular aspect of nature rests on the equivalence of its opposites." (Piet M Peintre," Art and Pure Plastic Art", 1937)
"For the state centralisation is the appropriate form of organisation, since it aims at the greatest possible uniformity in social life for the maintenance of political and social equilibrium. But for a movement whose very existence depends on prompt action at any favourable moment and on the independent thought and action of its supporters, centralism could but be a curse by weakening its power of decision and systematically repressing all immediate action. [...] Organisation is, after all, only a means to an end. When it becomes an end in itself, it kills the spirit and the vital initiative of its members and sets up that domination by mediocrity which is the characteristic of all bureaucracies." (Rudolf Rocker, "Anarcho-Syndicalism", 1938)
"One may generalize upon these processes in terms of group equilibrium. The group may be said to be in equilibrium when the interactions of its members fall into the customary pattern through which group activities are and have been organized. The pattern of interactions may undergo certain modifications without upsetting the group equilibrium, but abrupt and drastic changes destroy the equilibrium." (William F Whyte, "Street Corner Society", 1943)
"How would we express in terms of the statistical theory the marvelous faculty of a living organism, by which it delays the decay into thermodynamical equilibrium (death)? [...] the device by which an organism maintains itself stationary at a fairly high level of orderliness […] really consists in continually sucking orderliness from its environment." (Erwin Schrödinger, "What Is Life?", 1944)
"A well ordered society would be one where the State only had a negative action, comparable to that of a rudder: a light pressure at the right moment to counteract the first suggestion of any loss of equilibrium." (Simone Weil, "Gravity and Grace", 1947)
"The behavior of two individuals, consisting of effort which results in output, is considered to be determined by a satisfaction function which depends on remuneration (receiving part of the output) and on the effort expended. The total output of the two individuals is not additive, that is, together they produce in general more than separately. Each individual behaves in a way which he considers will maximize his satisfaction function. Conditions are deduced for a certain relative equilibrium and for the stability of this equilibrium, i.e., conditions under which it will not pay the individual to decrease his efforts. In the absence of such conditions ‘exploitation’ occurs which may or may not lead to total parasitism." (Anatol Rapoport, "Mathematical theory of motivation interactions of two individuals," The Bulletin of Mathematical Biophysics 9, 1947)
"The general method involved may be very simply stated. In cases where the equilibrium values of our variables can be regarded as the solutions of an extremum (maximum or minimum) problem, it is often possible regardless of the number of variables involved to determine unambiguously the qualitative behavior of our solution values in respect to changes of parameters." (Paul Samuelson, "Foundations of Economic Analysis", 1947)
"The study of the conditions for change begins appropriately with an analysis of the conditions for no change, that is, for the state of equilibrium." (Kurt Lewin, "Quasi-Stationary Social Equilibria and the Problem of Permanent Change", 1947)
"Now a system is said to be at equilibrium when it has no further tendency to change its properties." (Walter J Moore, "Physical chemistry", 1950)
"Physical irreversibility manifests itself in the fact that, whenever the system is in a state far removed from equilibrium, it is much more likely to move toward equilibrium, than in the opposite direction." (William Feller, "An Introduction To Probability Theory And Its Applications", 1950)
"Equilibrium requires that the whole of the structure, the form of its elements, and the means of interconnection be so combined that at the supports there will automatically be produced passive forces or reactions that are able to balance the forces acting upon the structures, including the force of its own weight." (Eduardo Torroja, "Philosophy of Structure", 1951)
"[…] there are three different but interconnected conceptions to be considered in every structure, and in every structural element involved: equilibrium, resistance, and stability." (Eduardo Torroja, "Philosophy of Structure" , 1951)
"Business-cycle theorists concerned themselves with why the economy naturally generated fluctuations in employment and output, [while the rest of the profession] continued to operate on the assumption that full employment was the natural, equilibrium position for the economy." (Robert A Gordon, "Business Fluctuations", 1952)
"Biological communities are systems of interacting components and thus display characteristic properties of systems, such as mutual interdependence, self-regulation, adaptation to disturbances, approach to states of equilibrium, etc." (Ludwig von Bertalanffy, "Problems of Life", 1952)
"Every stable system has the property that if displaced from a state of equilibrium and released, the subsequent movement is so matched to the initial displacement that the system is brought back to the state of equilibrium. A variety of disturbances will therefore evoke a variety of matched reactions." (W Ross Ashby, "Design for a Brain: The Origin of Adaptive Behavior", 1952)
"The primary fact is that all isolated state-determined dynamic systems are selective: from whatever state they have initially, they go towards states of equilibrium. These states of equilibrium are always characterised, in their relation to the change-inducing laws of the system, by being exceptionally resistant." (W Ross Ashby, "Design for a Brain: The Origin of Adaptive Behavior", 1952)
"Dynamic theory [...] shows how certain changes in the variables can be explained on the basis of [...] structural characteristics of the system. [...] The economy, of course, does not necessarily find an equilibrium position." (Wassily Leontief, "Studies in the Structure of the American Economy", 1953)
"Multiple equilibria are not necessarily useless, but from the standpoint of any exact science the existence of a uniquely determined equilibrium is, of course, of the utmost importance, even if proof has to be purchased at the price of very restrictive assumptions; without any possibility of proving the existence of (a) uniquely determined equilibrium - or at all events, of a small number of possible equilibria - at however high a level of abstraction, a field of phenomena is really a chaos that is not under analytical control." (Joseph A Schumpeter, "History of Economic Analysis", 1954)
"Perhaps as important is the relation between the existence of solutions to a competitive equilibrium and the problems of normative or welfare economics." (Kenneth J Arrow & Gerard Debreu. "Existence of an equilibrium for a competitive economy", Econometrica: Journal of the Econometric Society, 1954)
"As shorthand, when the phenomena are suitably simple, words such as equilibrium and stability are of great value and convenience. Nevertheless, it should be always borne in mind that they are mere shorthand, and that the phenomena will not always have the simplicity that these words presuppose." (W Ross Ashby, "An Introduction to Cybernetics", 1956)
"Reversible processes are not, in fact, processes at all, they are sequences of states of equilibrium. The processes which we encounter in real life are always irreversible processes." (Arnold Sommerfeld, "Thermodynamics and Statistical Mechanics", Lectures on Theoretical - Physics Vol. V, 1956)
"Multiple equilibria are not necessarily useless, but from the standpoint of any exact science the existence of a uniquely determined equilibrium is, of course, of the utmost importance, even if proof has to be purchased at the price of very restrictive assumptions; without any possibility of proving the existence of (a) uniquely determined equilibrium - or at all events, of a small number of possible equilibria - at however high a level of abstraction, a field of phenomena is really a chaos that is not under analytical control." (Joseph A Schumpeter, "History of Economic Analysis", 1954)
"Perhaps as important is the relation between the existence of solutions to a competitive equilibrium and the problems of normative or welfare economics." (Kenneth J Arrow & Gerard Debreu. "Existence of an equilibrium for a competitive economy", Econometrica: Journal of the Econometric Society, 1954)
"As shorthand, when the phenomena are suitably simple, words such as equilibrium and stability are of great value and convenience. Nevertheless, it should be always borne in mind that they are mere shorthand, and that the phenomena will not always have the simplicity that these words presuppose." (W Ross Ashby, "An Introduction to Cybernetics", 1956)
"Reversible processes are not, in fact, processes at all, they are sequences of states of equilibrium. The processes which we encounter in real life are always irreversible processes." (Arnold Sommerfeld, "Thermodynamics and Statistical Mechanics", Lectures on Theoretical - Physics Vol. V, 1956)
"Thus, if the whole is at a state of equilibrium, each part must be in a state of equilibrium in the conditions provided by the other. [...] the whole is at a state of equilibrium if and only if each part is at a state of equilibrium in the conditions provided by the other part. [...] No state (of the whole) can be a state of equilibrium unless it is acceptable to every one of the component parts, each acting in the conditions given by the others." (W Ross Ashby, "An Introduction to Cybernetics", 1956)
"It is clear to all that the animal organism is a highly complex system consisting of an almost infinite series of parts connected both with one another and, as a total complex, with the surrounding world, with which it is in a state of equilibrium. (Ivan P Pavlov, "Experimental psychology, and other essays", 1957)
"[Equilibrium] is a notion which can be employed usefully in varying degrees of looseness. It is an absolutely indispensable part of the toolbag of the economist and one which he can often contribute usefully to other sciences which are occasionally apt to get lost in the trackless exfoliations of purely dynamic systems." (Kenneth Boulding, The Skills of the Economist", Journal of Political Economy 67 (1), 1959)
"One of the most important skills of the economist, therefore, is that of simplification of the model." (Kenneth Boulding, "The Skills of the Economist", Journal of Political Economy 67 (1), 1959)
"The ability to work with systems of general equilibrium is perhaps one of the most important skills of the economist - a skill which he shares with many other scientists, but in which he has perhaps a certain comparative advantage." (Kenneth Boulding, "The Skills of the Economist", Journal of Political Economy 67 (1), 1959)
"The static stability of a system is defined by the initial tendency to return to equilibrium conditions following some disturbance from equilibrium. […] If the object has a tendency to continue in the direction of disturbance, negative static stability or static instability exists. […] If the object subject to disturbance has neither the tendency to return nor the tendency to continue in the displacement direction, neutral static stability exists." (Hugh H Hurt, "Aerodynamics for Naval Aviators", 1960)
"While static stability is concerned with the tendency of a displaced body to return to equilibrium, dynamic stability is concerned with the resulting motion with time. If an object is disturbed from equilibrium, the time history of the resulting motion indicates the dynamic stability of the system. In general, the system will demonstrate positive dynamic stability if the amplitude of the motion decreases with time." (Hugh H Hurt, "Aerodynamics for Naval Aviators", 1960)
"It is clear to all that the animal organism is a highly complex system consisting of an almost infinite series of parts connected both with one another and, as a total complex, with the surrounding world, with which it is in a state of equilibrium. (Ivan P Pavlov, "Experimental psychology, and other essays", 1957)
"[Equilibrium] is a notion which can be employed usefully in varying degrees of looseness. It is an absolutely indispensable part of the toolbag of the economist and one which he can often contribute usefully to other sciences which are occasionally apt to get lost in the trackless exfoliations of purely dynamic systems." (Kenneth Boulding, The Skills of the Economist", Journal of Political Economy 67 (1), 1959)
"One of the most important skills of the economist, therefore, is that of simplification of the model." (Kenneth Boulding, "The Skills of the Economist", Journal of Political Economy 67 (1), 1959)
"The ability to work with systems of general equilibrium is perhaps one of the most important skills of the economist - a skill which he shares with many other scientists, but in which he has perhaps a certain comparative advantage." (Kenneth Boulding, "The Skills of the Economist", Journal of Political Economy 67 (1), 1959)
"The static stability of a system is defined by the initial tendency to return to equilibrium conditions following some disturbance from equilibrium. […] If the object has a tendency to continue in the direction of disturbance, negative static stability or static instability exists. […] If the object subject to disturbance has neither the tendency to return nor the tendency to continue in the displacement direction, neutral static stability exists." (Hugh H Hurt, "Aerodynamics for Naval Aviators", 1960)
"While static stability is concerned with the tendency of a displaced body to return to equilibrium, dynamic stability is concerned with the resulting motion with time. If an object is disturbed from equilibrium, the time history of the resulting motion indicates the dynamic stability of the system. In general, the system will demonstrate positive dynamic stability if the amplitude of the motion decreases with time." (Hugh H Hurt, "Aerodynamics for Naval Aviators", 1960)
"A real system is subject to perturbations and it is never possible to control its initial state exactly. This raises the question of stability: under a slight perturbation will the system remain near the equilibrium state or not?" Joseph P LaSalle & Solomon Lefschetz, "Stability by Liapunov's Direct Method with Applications", 1961)
"An economy may be in equilibrium from a short-period point of view and yet contain within itself incompatibilities that are soon going to knock it out of equilibrium." (Joan Robinson, "Essays in the Theory of Economic Growth", 1965)
"[...] in a state of dynamic equilibrium with their environments. If they do not maintain this equilibrium they die; if they do maintain it they show a degree of spontaneity, variability, and purposiveness of response unknown in the non-living world. This is what is meant by ‘adaptation to environment’ […] [Its] essential feature […] is stability - that is, the ability to withstand disturbances." (Kenneth Craik, 'Living organisms', “The Nature of Psychology”, 1966)
"Higher, directed forms of energy (e.g., mechanical, electric, chemical) are dissipated, that is, progressively converted into the lowest form of energy, i.e., undirected heat movement of molecules; chemical systems tend toward equilibria with maximum entropy; machines wear out owing to friction; in communication channels, information can only be lost by conversion of messages into noise but not vice versa, and so forth." (Ludwig von Bertalanffy, "Robots, Men and Minds", 1967)
"[The equilibrium model describes systems] which, in moving to an equilibrium point, typically lose organization, and then tend to hold that minimum level within relatively narrow conditions of disturbance." (Walter F Buckley, "Sociology and modern systems theory", 1967)
"A more viable model, one much more faithful to the kind of system that society is more and more recognized to be, is in process of developing out of, or is in keeping with, the modern systems perspective (which we use loosely here to refer to general systems research, cybernetics, information and communication theory, and related fields). Society, or the sociocultural system, is not, then, principally an equilibrium system or a homeostatic system, but what we shall simply refer to as a complex adaptive system." (Walter F Buckley, "Society as a complex adaptive system", 1968)
"Biologically, life is not maintenance or restoration of equilibrium but is essentially maintenance of disequilibria, as the doctrine of the organism as open system reveals. Reaching equilibrium means death and consequent decay. Psychologically, behaviour not only tends to release tensions but also builds up tensions; if this stops, the patient is a decaying mental corpse in the same way a living organism becomes a body in decay when tensions and forces keeping it from equilibrium have stopped." (Ludwig von Bertalanffy, "General System Theory", 1968)
"Conventional physics deals only with closed systems, i.e. systems which are considered to be isolated from their environment. [...] However, we find systems which by their very nature and definition are not closed systems. Every living organism is essentially an open system. It maintains itself in a continuous inflow and outflow, a building up and breaking down of components, never being, so long as it is alive, in a state of chemical and thermodynamic equilibrium but maintained in a so-called steady state which is distinct from the latter." (Ludwig von Bertalanffy, "General System Theory", 1968)
"We have argued at some length in another place that the mechanical equilibrium model and the organismic homeostasis models of society that have underlain most modern sociological theory have outlived their usefulness." (Walter F Buckley, "Society as a complex adaptive system", 1968)
"Peace is an unstable equilibrium, which can be preserved only by acknowledged supremacy or equal power." (Will Durant, The Lessons of History, 1968)
"An economy may be in equilibrium from a short-period point of view and yet contain within itself incompatibilities that are soon going to knock it out of equilibrium." (Joan Robinson, "Essays in the Theory of Economic Growth", 1965)
"[...] in a state of dynamic equilibrium with their environments. If they do not maintain this equilibrium they die; if they do maintain it they show a degree of spontaneity, variability, and purposiveness of response unknown in the non-living world. This is what is meant by ‘adaptation to environment’ […] [Its] essential feature […] is stability - that is, the ability to withstand disturbances." (Kenneth Craik, 'Living organisms', “The Nature of Psychology”, 1966)
"Higher, directed forms of energy (e.g., mechanical, electric, chemical) are dissipated, that is, progressively converted into the lowest form of energy, i.e., undirected heat movement of molecules; chemical systems tend toward equilibria with maximum entropy; machines wear out owing to friction; in communication channels, information can only be lost by conversion of messages into noise but not vice versa, and so forth." (Ludwig von Bertalanffy, "Robots, Men and Minds", 1967)
"[The equilibrium model describes systems] which, in moving to an equilibrium point, typically lose organization, and then tend to hold that minimum level within relatively narrow conditions of disturbance." (Walter F Buckley, "Sociology and modern systems theory", 1967)
"A more viable model, one much more faithful to the kind of system that society is more and more recognized to be, is in process of developing out of, or is in keeping with, the modern systems perspective (which we use loosely here to refer to general systems research, cybernetics, information and communication theory, and related fields). Society, or the sociocultural system, is not, then, principally an equilibrium system or a homeostatic system, but what we shall simply refer to as a complex adaptive system." (Walter F Buckley, "Society as a complex adaptive system", 1968)
"Biologically, life is not maintenance or restoration of equilibrium but is essentially maintenance of disequilibria, as the doctrine of the organism as open system reveals. Reaching equilibrium means death and consequent decay. Psychologically, behaviour not only tends to release tensions but also builds up tensions; if this stops, the patient is a decaying mental corpse in the same way a living organism becomes a body in decay when tensions and forces keeping it from equilibrium have stopped." (Ludwig von Bertalanffy, "General System Theory", 1968)
"Conventional physics deals only with closed systems, i.e. systems which are considered to be isolated from their environment. [...] However, we find systems which by their very nature and definition are not closed systems. Every living organism is essentially an open system. It maintains itself in a continuous inflow and outflow, a building up and breaking down of components, never being, so long as it is alive, in a state of chemical and thermodynamic equilibrium but maintained in a so-called steady state which is distinct from the latter." (Ludwig von Bertalanffy, "General System Theory", 1968)
"We have argued at some length in another place that the mechanical equilibrium model and the organismic homeostasis models of society that have underlain most modern sociological theory have outlived their usefulness." (Walter F Buckley, "Society as a complex adaptive system", 1968)
"Peace is an unstable equilibrium, which can be preserved only by acknowledged supremacy or equal power." (Will Durant, The Lessons of History, 1968)
"A precise, all-encompassing definition is difficult to frame, but the general meaning of 'equilibrium' is that a system has settled down to the point where its macroscopic properties are unchanging with time. In practice there is seldom any doubt whether a system has reached equilibrium or not. And there is always a test of sorts: do the macroscopic properties, given further 'aging'' of the system, change discernibly?" (Ralph Baierlein, "Atoms and Information Theory: An Introduction to Statistical Mechanics", 1971)
"A system is in equilibrium when the forces constituting it are arranged in such a way as to compensate each other, like the two weights pulling at the arms of a pair of scales." (Rudolf Arnheim, "Entropy and Art: An Essay on Disorder and Order", 1971)
"When matter is becoming disturbed by non-equilibrium conditions it organizes itself, it wakes up. It happens that our world is a non-equilibrium system." (Ilya Prigogine, "Thermodynamics of Evolution", 1972)
"In an isolated system, which cannot exchange energy and matter with the surroundings, this tendency is expressed in terms of a function of the macroscopic state of the system: the entropy." (Ilya Prigogine, "Thermodynamics of Evolution", 1972)
"The evolution of a physicochemical system leads to an equilibrium state of maximum disorder." (Ilya Prigogine, "Thermodynamics of Evolution", 1972)
"The functional order maintained within living systems seems to defy the Second Law; nonequilibrium thermodynamics describes how such systems come to terms with entropy." (Ilya Prigogine, "Thermodynamics of Evolution", 1972)
"There is little point in demanding minor concessions and relaxations of the abstract, timeless general equilibrium. The light it can throw on human affairs is throw by its most austere and formal version. We are not concerned to ask: How could it possibly work? The useful question is: What does its logical structure imply?" (George L S Shackle, "Epistemics and Economics", 1972)
"Chance is commonly viewed as a self-correcting process in which a deviation in one direction induces a deviation in the opposite direction to restore the equilibrium. In fact, deviations are not 'corrected' as a chance process unfolds, they are merely diluted." (Amos Tversky, "Judgment Under Uncertainty: Heuristics and Biases", 1974)
"Equilibrium is a figment of the human imagination." (Kenneth Boulding, Toward a General Social Science, 1974)
"The vector equilibrium is the true zero reference of the energetic mathematics. Zero pulsation in the vector equilibrium is the nearest approach we will ever know to eternity and god: the zero phase of conceptual integrity inherent in the positive and negative asymmetries that propagate the differentials of consciousness." (Buckminster Fuller, "Synergetics: Explorations in the Geometry of Thinking", 1975)
"The notion that the 'balance of nature' is delicately poised and easily upset is nonsense. Nature is extraordinarily tough and resilient, interlaced with checks and balances, with an astonishing capacity for recovering from disturbances in equilibrium. The formula for survival is not power; it is symbiosis." (Sir Eric Ashby, [Encounter] 1976)
"A system is in equilibrium when the forces constituting it are arranged in such a way as to compensate each other, like the two weights pulling at the arms of a pair of scales." (Rudolf Arnheim, "Entropy and Art: An Essay on Disorder and Order", 1971)
"When matter is becoming disturbed by non-equilibrium conditions it organizes itself, it wakes up. It happens that our world is a non-equilibrium system." (Ilya Prigogine, "Thermodynamics of Evolution", 1972)
"In an isolated system, which cannot exchange energy and matter with the surroundings, this tendency is expressed in terms of a function of the macroscopic state of the system: the entropy." (Ilya Prigogine, "Thermodynamics of Evolution", 1972)
"The evolution of a physicochemical system leads to an equilibrium state of maximum disorder." (Ilya Prigogine, "Thermodynamics of Evolution", 1972)
"The functional order maintained within living systems seems to defy the Second Law; nonequilibrium thermodynamics describes how such systems come to terms with entropy." (Ilya Prigogine, "Thermodynamics of Evolution", 1972)
"There is little point in demanding minor concessions and relaxations of the abstract, timeless general equilibrium. The light it can throw on human affairs is throw by its most austere and formal version. We are not concerned to ask: How could it possibly work? The useful question is: What does its logical structure imply?" (George L S Shackle, "Epistemics and Economics", 1972)
"Chance is commonly viewed as a self-correcting process in which a deviation in one direction induces a deviation in the opposite direction to restore the equilibrium. In fact, deviations are not 'corrected' as a chance process unfolds, they are merely diluted." (Amos Tversky, "Judgment Under Uncertainty: Heuristics and Biases", 1974)
"Equilibrium is a figment of the human imagination." (Kenneth Boulding, Toward a General Social Science, 1974)
"The vector equilibrium is the true zero reference of the energetic mathematics. Zero pulsation in the vector equilibrium is the nearest approach we will ever know to eternity and god: the zero phase of conceptual integrity inherent in the positive and negative asymmetries that propagate the differentials of consciousness." (Buckminster Fuller, "Synergetics: Explorations in the Geometry of Thinking", 1975)
"The notion that the 'balance of nature' is delicately poised and easily upset is nonsense. Nature is extraordinarily tough and resilient, interlaced with checks and balances, with an astonishing capacity for recovering from disturbances in equilibrium. The formula for survival is not power; it is symbiosis." (Sir Eric Ashby, [Encounter] 1976)
"In any system governed by a potential, and in which the system's behavior is determined by no more than four different factors, only seven qualitatively different types of discontinuity are possible. In other words, while there are an infinite number of ways for such a system to change continuously (staying at or near equilibrium), there are only seven structurally stable ways for it to change discontinuously (passing through non-equilibrium states)." (Alexander Woodcock & Monte Davis, "Catastrophe Theory", 1978)
"We know, in other words, the general conditions in which what we call, somewhat misleadingly, an equilibrium will establish itself: but we never know what the particular prices or wages are which would exist if the market were to bring about such an equilibrium." (Friedrich Hayek, "Unemployment and monetary policy: government as generator of the ‘business cycle’", 1979)
"The equilibrium between supply and demand is achieved only through a reaction against the upsetting of the equilibrium." (David Harvey, "The Limits To Capital", 1982)
"All environmental areas, from the primeval forest to the large city, can be regarded as ecosystems and investigated accordingly, most of the attention being given to the lasting existence and functioning or 'equilibrium' of these systems." (Wolfgang Haber, Universitas: A Quarterly German Review of the Arts and Sciences Vol.26 (2), 1984)
"If a system is in a state of equilibrium (a steady state), then all sub-systems must be in equilibrium. If all sub-systems are in a state of equilibrium, then the system must be in equilibrium." (Barry Clemson, "Cybernetics: A New Management Tool", 1984)
"Multiple discoveries are in fact very common in science and for much the same reason. Developments in related fields with different motivation help one to understand a difficult problem better. Since these developments are public knowledge, many scholars can take advantage of them. It is pleasant to the ego to be first or among the first with a new discovery. However, in this case at least, the evidence is clear that the development of general equilibrium theory would have gone on quite as it did without me." (Kenneth Arrow, 1984)
"Economic theory is devoted to the study of equilibrium positions. The concept of equilibrium is very useful. It allows us to focus on the final outcome rather than the process that leads up to it. But the concept is also very deceptive. It has the aura of something empirical: since the adjustment process is supposed to lead to an equilibrium, an equilibrium position seems somehow implicit in our observations. That is not true. Equilibrium itself has rarely been observed in real life - market prices have a notorious habit of fluctuating." (George Soros, "The Alchemy of Finance: Reading the Mind of the Market", 1987)
"The concept of a general equilibrium has no relevance to the real world (in other words, classical economics is an exercise in futility)." (George Soros, "The Alchemy of Finance: Reading the Mind of the Market", 1987)
"The most abstract conservation laws of physics come into their being in describing equilibrium in the most extreme conditions. They are the most rigorous conservation laws, the last to break down. The more extreme the conditions, the fewer the conserved structures. [...] In a deep sense, we understand the interior of the sun better that the interior of the earth, and the early stages of the big bang best of all." (Frank Wilczek, "Longing for the Harmonies: Themes and Variations from Modern Physics", 1987)
"When loops are present, the network is no longer singly connected and local propagation schemes will invariably run into trouble. [...] If we ignore the existence of loops and permit the nodes to continue communicating with each other as if the network were singly connected, messages may circulate indefinitely around the loops and process may not converges to a stable equilibrium. […] Such oscillations do not normally occur in probabilistic networks […] which tend to bring all messages to some stable equilibrium as time goes on. However, this asymptotic equilibrium is not coherent, in the sense that it does not represent the posterior probabilities of all nodes of the network." (Judea Pearl, "Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference", 1988)
"Living systems are never in equilibrium. They are inherently unstable. They may seem stable, but they're not. Everything is moving and changing. In a sense, everything is on the edge of collapse. Michael Crichton, "Jurassic Park", 1990)
"History has so far shown us only two roads to international stability: domination and equilibrium."(Henry Kissinger, [Times] 1991)
"We know, in other words, the general conditions in which what we call, somewhat misleadingly, an equilibrium will establish itself: but we never know what the particular prices or wages are which would exist if the market were to bring about such an equilibrium." (Friedrich Hayek, "Unemployment and monetary policy: government as generator of the ‘business cycle’", 1979)
"The equilibrium between supply and demand is achieved only through a reaction against the upsetting of the equilibrium." (David Harvey, "The Limits To Capital", 1982)
"All environmental areas, from the primeval forest to the large city, can be regarded as ecosystems and investigated accordingly, most of the attention being given to the lasting existence and functioning or 'equilibrium' of these systems." (Wolfgang Haber, Universitas: A Quarterly German Review of the Arts and Sciences Vol.26 (2), 1984)
"If a system is in a state of equilibrium (a steady state), then all sub-systems must be in equilibrium. If all sub-systems are in a state of equilibrium, then the system must be in equilibrium." (Barry Clemson, "Cybernetics: A New Management Tool", 1984)
"Multiple discoveries are in fact very common in science and for much the same reason. Developments in related fields with different motivation help one to understand a difficult problem better. Since these developments are public knowledge, many scholars can take advantage of them. It is pleasant to the ego to be first or among the first with a new discovery. However, in this case at least, the evidence is clear that the development of general equilibrium theory would have gone on quite as it did without me." (Kenneth Arrow, 1984)
"Economic theory is devoted to the study of equilibrium positions. The concept of equilibrium is very useful. It allows us to focus on the final outcome rather than the process that leads up to it. But the concept is also very deceptive. It has the aura of something empirical: since the adjustment process is supposed to lead to an equilibrium, an equilibrium position seems somehow implicit in our observations. That is not true. Equilibrium itself has rarely been observed in real life - market prices have a notorious habit of fluctuating." (George Soros, "The Alchemy of Finance: Reading the Mind of the Market", 1987)
"The concept of a general equilibrium has no relevance to the real world (in other words, classical economics is an exercise in futility)." (George Soros, "The Alchemy of Finance: Reading the Mind of the Market", 1987)
"The most abstract conservation laws of physics come into their being in describing equilibrium in the most extreme conditions. They are the most rigorous conservation laws, the last to break down. The more extreme the conditions, the fewer the conserved structures. [...] In a deep sense, we understand the interior of the sun better that the interior of the earth, and the early stages of the big bang best of all." (Frank Wilczek, "Longing for the Harmonies: Themes and Variations from Modern Physics", 1987)
"When loops are present, the network is no longer singly connected and local propagation schemes will invariably run into trouble. [...] If we ignore the existence of loops and permit the nodes to continue communicating with each other as if the network were singly connected, messages may circulate indefinitely around the loops and process may not converges to a stable equilibrium. […] Such oscillations do not normally occur in probabilistic networks […] which tend to bring all messages to some stable equilibrium as time goes on. However, this asymptotic equilibrium is not coherent, in the sense that it does not represent the posterior probabilities of all nodes of the network." (Judea Pearl, "Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference", 1988)
"Living systems are never in equilibrium. They are inherently unstable. They may seem stable, but they're not. Everything is moving and changing. In a sense, everything is on the edge of collapse. Michael Crichton, "Jurassic Park", 1990)
"History has so far shown us only two roads to international stability: domination and equilibrium."(Henry Kissinger, [Times] 1991)
"[...] it's essentially meaningless to talk about a complex adaptive system being in equilibrium: the system can never get there. It is always unfolding, always in transition. In fact, if the system ever does reach equilibrium, it isn't just stable. It's dead." (M Mitchell Waldrop, "Complexity: The Emerging Science at the Edge of Order and Chaos", 1992)
"Democracy is the only system capable of reflecting the humanist premise of equilibrium or balance. The key to its secret is the involvement of the citizen." (John R Saul, "The Doubter's Companion", 1994)
"In many parts of the economy, stabilizing forces appear not to operate. Instead, positive feedback magnifies the effects of small economic shifts; the economic models that describe such effects differ vastly from the conventional ones. Diminishing returns imply a single equilibrium point for the economy, but positive feedback – increasing returns – makes for many possible equilibrium points. There is no guarantee that the particular economic outcome selected from among the many alternatives will be the ‘best’ one." (W Brian Arthur, "Returns and Path Dependence in the Economy", 1994)
"Objects in nature have provided and do provide models for stimulating mathematical discoveries. Nature has a way of achieving an equilibrium and an exquisite balance in its creations. The key to understanding the workings of nature is with mathematics and the sciences. [.] Mathematical tools provide a means by which we try to understand, explain, and copy natural phenomena. One discovery leads to the next." (Theoni Pappas, "The Magic of Mathematics: Discovering the spell of mathematics", 1994)
"The model of competitive equilibrium which has been discussed so far is set in a timeless environment. People and companies all operate in a world in which there is no future and hence no uncertainty." (Paul Ormerod, "The Death of Economics", 1994)
"We need to abandon the economist's notion of the economy as a machine, with its attendant concept of equilibrium. A more helpful way of thinking about the economy is to imagine it as a living organism." (Paul Ormerod, "The Death of Economics", 1994)
"Regarding stability, the state trajectories of a system tend to equilibrium. In the simplest case they converge to one point (or different points from different initial states), more commonly to one (or several, according to initial state) fixed point or limit cycle(s) or even torus(es) of characteristic equilibrial behaviour. All this is, in a rigorous sense, contingent upon describing a potential, as a special summation of the multitude of forces acting upon the state in question, and finding the fixed points, cycles, etc., to be minima of the potential function. It is often more convenient to use the equivalent jargon of 'attractors' so that the state of a system is 'attracted' to an equilibrial behaviour. In any case, once in equilibrial conditions, the system returns to its limit, equilibrial behaviour after small, arbitrary, and random perturbations."
"Systems, acting dynamically, produce (and incidentally, reproduce) their own boundaries, as structures which are complementary (necessarily so) to their motion and dynamics. They are liable, for all that, to instabilities chaos, as commonly interpreted of chaotic form, where nowadays, is remote from the random. Chaos is a peculiar situation in which the trajectories of a system, taken in the traditional sense, fail to converge as they approach their limit cycles or 'attractors' or 'equilibria'. Instead, they diverge, due to an increase, of indefinite magnitude, in amplification or gain."
"Democracy is the only system capable of reflecting the humanist premise of equilibrium or balance. The key to its secret is the involvement of the citizen." (John R Saul, "The Doubter's Companion", 1994)
"In many parts of the economy, stabilizing forces appear not to operate. Instead, positive feedback magnifies the effects of small economic shifts; the economic models that describe such effects differ vastly from the conventional ones. Diminishing returns imply a single equilibrium point for the economy, but positive feedback – increasing returns – makes for many possible equilibrium points. There is no guarantee that the particular economic outcome selected from among the many alternatives will be the ‘best’ one." (W Brian Arthur, "Returns and Path Dependence in the Economy", 1994)
"Objects in nature have provided and do provide models for stimulating mathematical discoveries. Nature has a way of achieving an equilibrium and an exquisite balance in its creations. The key to understanding the workings of nature is with mathematics and the sciences. [.] Mathematical tools provide a means by which we try to understand, explain, and copy natural phenomena. One discovery leads to the next." (Theoni Pappas, "The Magic of Mathematics: Discovering the spell of mathematics", 1994)
"The model of competitive equilibrium which has been discussed so far is set in a timeless environment. People and companies all operate in a world in which there is no future and hence no uncertainty." (Paul Ormerod, "The Death of Economics", 1994)
"We need to abandon the economist's notion of the economy as a machine, with its attendant concept of equilibrium. A more helpful way of thinking about the economy is to imagine it as a living organism." (Paul Ormerod, "The Death of Economics", 1994)
"Initially, it may seem that such systems constitute a very special class of processes. And, in fact, that is indeed the case. However, nature has providentially worked things out so that a lot of processes of practical concern just happen to belong to this class - including many of the systems of classical physics like passive electrical circuits, damped vibrating springs, and bending beams. Moreover, when we observe these kinds of processes in real life, what we usually see is the system when it is at or very near to equilibrium. For these reasons catastrophe theory can be of great value in helping us understand how these kinds of systems can shift abruptly from one equilibrium state to another as various parameters, like spring constants or unemployment rates, are varied just a little bit." (John L Casti, "Five Golden Rules", 1995)
"Self-organization refers to the spontaneous formation of patterns and pattern change in open, nonequilibrium systems. […] Self-organization provides a paradigm for behavior and cognition, as well as the structure and function of the nervous system. In contrast to a computer, which requires particular programs to produce particular results, the tendency for self-organization is intrinsic to natural systems under certain conditions." (J A Scott Kelso, "Dynamic Patterns : The Self-organization of Brain and Behavior", 1995)"The reason catastrophe theory can tell us about such abrupt changes in a system's behavior is that we usually observe a dynamical system when it's at or near its steady-state, or equilibrium, position. And under various assumptions about the nature of the system's dynamical law of motion, the set of all possible equilibrium states is simply the set of critical points of a smooth function closely related to the system dynamics. When these critical points are nondegenerate, Morse's Theorem applies. But it is exactly when they become degenerate that the system can move sharply from one equilibrium position to another. The Thorn Classification Theorem tells when such shifts will occur and what direction they will take." (John L Casti, "Five Golden Rules", 1995)
"Economic theory in general ignores processes which take time to occur, and instead assumes that everything occurs in equilibrium." (Steve Keen, "Naked Emperor Of The Social Sciences", 2001)
"The obsession with equilibrium has imposed enormous costs on economics." (Steve Keen, "Debunking Economics - The Naked Emperor Of The Social Sciences", 2001)
"In this crucial sense, the theory of punctuated equilibrium adopts a very conservative position. The theory asserts no novel claim about modes or mechanisms of speciation; punctuated equilibrium merely takes a standard microevolutionary model and elucidates its expected expression when properly scaled into geological time." (Stephen J Gould, "The Structure of Evolutionary Theory", 2002)
"Positive feedbacks, when unchecked, can produce runaways until the deviation from equilibrium is so large that other effects can be abruptly triggered and lead to ruptures and crashes." (Didier Sornette, "Why Stock Markets Crash - Critical Events in Complex Systems", 2003)
"Stock market bubbles don't grow out of thin air. They have a solid basis in reality - but reality as distorted by a misconception. Under normal conditions misconceptions are self-correcting, and the markets tend toward some kind of equilibrium. Occasionally, a misconception is reinforced by a trend prevailing in reality, and that is when a boom-bust process gets under way. Eventually the gap between reality and its false interpretation becomes unsustainable, and the bubble bursts." (George Soros, [interview] 2004)
"The players in a game are said to be in strategic equilibrium (or simply equilibrium) when their play is mutually optimal: when the actions and plans of each player are rational in the given strategic environment - i. e., when each knows the actions and plans of the others." (Robert Aumann, "War and Peace", 2005)
"Contrary to what happens at equilibrium, or near equilibrium, systems far from equilibrium do not conform to any minimum principle that is valid for functions of free energy or entropy production." (Ilya Prigogine, "The End of Certainty: Time, Chaos, and the New Laws of Nature", 1996)
"[…] self-organization is the spontaneous emergence of new structures and new forms of behavior in open systems far from equilibrium, characterized by internal feedback loops and described mathematically by nonlinear equations.” (Fritjof Capra, “The web of life: a new scientific understanding of living systems”, 1996)
"Complex systems operate under conditions far from equilibrium. Complex systems need a constant flow of energy to change, evolve and survive as complex entities. Equilibrium, symmetry and complete stability mean death. Just as the flow, of energy is necessary to fight entropy and maintain the complex structure of the system, society can only survive as a process. It is defined not by its origins or its goals, but by what it is doing." (Paul Cilliers,"Complexity and Postmodernism: Understanding Complex Systems", 1998)
"Financial markets are supposed to swing like a pendulum: They may fluctuate wildly in response to exogenous shocks, but eventually they are supposed to come to rest at an equilibrium point and that point is supposed to be the same irrespective of the interim fluctuations." (George Soros, "The Crisis of Global Capitalism", 1998)
"There has to be a constant flow of energy to maintain the organization of the system and to ensure its survival. Equilibrium is another word for death." (Paul Cilliers, "Complexity and Postmodernism", 1998)
"An equilibrium is not always an optimum; it might not even be good. This may be the most important discovery of game theory." (Ivar Ekeland, "Le meilleur des mondes possibles" ["The Best of All Possible Worlds"], 2000)
"[…] self-organization is the spontaneous emergence of new structures and new forms of behavior in open systems far from equilibrium, characterized by internal feedback loops and described mathematically by nonlinear equations.” (Fritjof Capra, “The web of life: a new scientific understanding of living systems”, 1996)
"Complex systems operate under conditions far from equilibrium. Complex systems need a constant flow of energy to change, evolve and survive as complex entities. Equilibrium, symmetry and complete stability mean death. Just as the flow, of energy is necessary to fight entropy and maintain the complex structure of the system, society can only survive as a process. It is defined not by its origins or its goals, but by what it is doing." (Paul Cilliers,"Complexity and Postmodernism: Understanding Complex Systems", 1998)
"Financial markets are supposed to swing like a pendulum: They may fluctuate wildly in response to exogenous shocks, but eventually they are supposed to come to rest at an equilibrium point and that point is supposed to be the same irrespective of the interim fluctuations." (George Soros, "The Crisis of Global Capitalism", 1998)
"There has to be a constant flow of energy to maintain the organization of the system and to ensure its survival. Equilibrium is another word for death." (Paul Cilliers, "Complexity and Postmodernism", 1998)
"An equilibrium is not always an optimum; it might not even be good. This may be the most important discovery of game theory." (Ivar Ekeland, "Le meilleur des mondes possibles" ["The Best of All Possible Worlds"], 2000)
"Periods of rapid change and high exponential growth do not, typically, last long. A new equilibrium with a new dominant technology and/or competitor is likely to be established before long. Periods of punctuation are therefore exciting and exhibit unusual uncertainty. The payoff from establishing a dominant position in this short time is therefore extraordinarily high. Dominance is more likely to come from skill in marketing and positioning than from superior technology itself." (Richar Koch, "The Power Laws", 2000)
"Broadly speaking two major approaches to dynamic discontinuities have developed within mathematics. They share the idea of bifurcation, or the splitting of equilibria at critical points, and also generally the idea that many important dynamically functional relationships exhibit nonlinearity rather than linearity. They differ in focusing on large-scale or on small-scale discontinuities." (J Barkley Rosser Jr, "From Catastrophe to Chaos: A General Theory of Economic Discontinuities" 2nd Ed., 2000)
"Economic theory in general ignores processes which take time to occur, and instead assumes that everything occurs in equilibrium." (Steve Keen, "Naked Emperor Of The Social Sciences", 2001)
"The obsession with equilibrium has imposed enormous costs on economics." (Steve Keen, "Debunking Economics - The Naked Emperor Of The Social Sciences", 2001)
"In this crucial sense, the theory of punctuated equilibrium adopts a very conservative position. The theory asserts no novel claim about modes or mechanisms of speciation; punctuated equilibrium merely takes a standard microevolutionary model and elucidates its expected expression when properly scaled into geological time." (Stephen J Gould, "The Structure of Evolutionary Theory", 2002)
"Positive feedbacks, when unchecked, can produce runaways until the deviation from equilibrium is so large that other effects can be abruptly triggered and lead to ruptures and crashes." (Didier Sornette, "Why Stock Markets Crash - Critical Events in Complex Systems", 2003)
"Stock market bubbles don't grow out of thin air. They have a solid basis in reality - but reality as distorted by a misconception. Under normal conditions misconceptions are self-correcting, and the markets tend toward some kind of equilibrium. Occasionally, a misconception is reinforced by a trend prevailing in reality, and that is when a boom-bust process gets under way. Eventually the gap between reality and its false interpretation becomes unsustainable, and the bubble bursts." (George Soros, [interview] 2004)
"The players in a game are said to be in strategic equilibrium (or simply equilibrium) when their play is mutually optimal: when the actions and plans of each player are rational in the given strategic environment - i. e., when each knows the actions and plans of the others." (Robert Aumann, "War and Peace", 2005)
"[...] the scientific models of concrete things are symbolic rather than iconic: they are systems of propositions, not pictures. Besides, such models are seldom if ever completely accurate, if only because they involve more or less brutal simplifications, such as pretending that a metallic surface is smooth, a crystal has no impurities, a biopopulation has a single predator, or a market is in equilibrium. These are all fictions. However, they are stylizations rather than wild fantasies. Hence, introducing and using them to account for real existents does not commit us to fictionism, just as defending the role of experience need not make us empiricists, nor is admitting the role of intuition enough to qualify as intuitionist." (Mario Bunge, "Chasing Reality: Strife over Realism", 2006)
"Global stability of an equilibrium removes the restrictions on the initial conditions. In global asymptotic stability, solutions approach the equilibrium for all initial conditions. [...] In a study of local stability, first equilibrium solutions are identified, then linearization techniques are applied to determine the behavior of solutions near the equilibrium. If the equilibrium is stable for any set of initial conditions, then this type of stability is referred to as global stability." (Linda J S Allen, "An Introduction to Mathematical Biology", 2007)
"The second law of thermodynamics states that in an isolated system, entropy can only increase, not decrease. Such systems evolve to their state of maximum entropy, or thermodynamic equilibrium. Therefore, physical self-organizing systems cannot be isolated: they require a constant input of matter or energy with low entropy, getting rid of the internally generated entropy through the output of heat ('dissipation'). This allows them to produce ‘dissipative structures’ which maintain far from thermodynamic equilibrium. Life is a clear example of order far from thermodynamic equilibrium." (Carlos Gershenson, "Design and Control of Self-organizing Systems", 2007)
"The invisible hand is an emergent property of this system, which never reaches an optimal equilibrium, but instead is fundamentally dynamic and unstable, with complex effects on society." (David Orrell, "The Other Side Of The Coin", 2008)
"The second law of thermodynamics states that in an isolated system, entropy can only increase, not decrease. Such systems evolve to their state of maximum entropy, or thermodynamic equilibrium. Therefore, physical self-organizing systems cannot be isolated: they require a constant input of matter or energy with low entropy, getting rid of the internally generated entropy through the output of heat ('dissipation'). This allows them to produce ‘dissipative structures’ which maintain far from thermodynamic equilibrium. Life is a clear example of order far from thermodynamic equilibrium." (Carlos Gershenson, "Design and Control of Self-organizing Systems", 2007)
"The invisible hand is an emergent property of this system, which never reaches an optimal equilibrium, but instead is fundamentally dynamic and unstable, with complex effects on society." (David Orrell, "The Other Side Of The Coin", 2008)
"Cybernetics is the art of creating equilibrium in a world of possibilities and constraints. This is not just a romantic description, it portrays the new way of thinking quite accurately. Cybernetics differs from the traditional scientific procedure, because it does not try to explain phenomena by searching for their causes, but rather by specifying the constraints that determine the direction of their development." (Ernst von Glasersfeld, "Partial Memories: Sketches from an Improbable Life", 2010)
"In dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behaviour. Generally, at a bifurcation, the local stability properties of equilibria, periodic orbits or other invariant sets changes." (Gregory Faye, "An introduction to bifurcation theory", 2011)
"Social scientists use the term 'equilibrium' to describe balance between opposing forces, say, supply and demand, so small disturbances or deviations in one direction, like those of a pendulum, would be countered with an adjustment in the opposite direction that would bring things back to stability."
"An equilibrium is defined to be stable if all sufficiently small disturbances away from it damp out in time. Thus stable equilibria are represented geometrically by stable fixed points. Conversely, unstable equilibria, in which disturbances grow in time, are represented by unstable fixed points." (Steven H Strogatz, "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering", 2015)
"Change is real; the unchanging is an illusion. Classical science focused on systems that were in equilibrium whereas modern science also looks at states that may be far from equilibrium. Equilibrium situations can give you the feeling that things are unchanging but this is always only a temporary condition. Equilibriums beak down and when they do, when the system is far from equilibrium, then the dynamism of the system is most visible. In such situations one is studying change directly." (William Byers, "Deep Thinking: What Mathematics Can Teach Us About the Mind", 2015)
"[…] chaos and fractals are part of an even grander subject known as dynamics. This is the subject that deals with change, with systems that evolve in time. Whether the system in question settles down to equilibrium, keeps repeating in cycles, or does something more complicated, it is dynamics that we use to analyze the behavior."
"To remedy chaotic situations requires a chaotic approach, one that is non-linear, constantly morphing, and continually sharpening its competitive edge with recurring feedback loops that build upon past experiences and lessons learned. Improvement cannot be sustained without reflection. Chaos arises from myriad sources that stem from two origins: internal chaos rising within you, and external chaos being imposed upon you by the environment. The result of this push/pull effect is the disequilibrium [...]." (Jeff Boss, "Navigating Chaos: How to Find Certainty in Uncertain Situations", 2015)
"There must be a double method for solving mechanical problems: one is the direct method founded on the laws of equilibrium or of motion; but the other one is by knowing which formula must provide a maximum or a minimum. The former way proceeds by efficient causes: both ways lead to the same solution, and it is such a harmony which convinces us of the truth of the solution, even if each method has to be separately founded on indubitable principles. But is often very difficult to discover the formula which must be a maximum or minimum, and by which the quantity of action is represented." (Leonhard Euler)
"The world is not dialectical - it is sworn to extremes, not to equilibrium, sworn to radical antagonism, not to reconciliation or synthesis." (Jean Baudrillard)
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